My thoughts on story/characters/suspects so far
First of all, I'm really enjoying the game so far, telltale is doing a great job 
That being said, I stumbled upon this forum on accident and after reading multiple threads I was surprised how very few people notice things that - at least for me - struck as obvious. So I decided to share some of thoughts/theories with you guys
Before I begin, I'd like to introduce you to the term mindfuck - Something that intentionally destabilizes, confuses or manipulates the mind of another person. http://en.wiktionary.org/wiki/mindfuck
It is a technique used in multiple movies and detective novels that make you think obvious while carefully giving you the clues of what is actually happening (in other words, you end up with something totally unexpected at the end, but once you know the end and you rewatch/reread the hole thing everything kinda starts to make sense).
That being said, my theory of what is happening:
As we all know, only fables who look like human or can afford to look like human live in human populated environment - others live in secluded and prison-like farm. Very few of the fables lead a happy life - in fact, most of the fables we are introduced to struggle to survive in this harsh world and would like to see some changes - changes which won't happen under current deputy mayor.
At the very start of the game we are introduced to Woody. He is a drunk who can be impulsive and violent, but I believe his character would simply be unable to kill anyone. Let's face it, it took him a long time to build up courage to try and rob the Little Red Hood - and he seems genuinely surprised by the fact that Faith was killed. Besides, he is a friend to Holly which in my eyes totally rules him out of possible Lilys killers.Lastly, he has no motive whatsoever to leave heads in front of Bigbys apartment - he may have a grudge against Bigby, but as he says himself in the pub he is tired of all the endless fighting with our protagonist.
How does he get into this murder situation? First of all, I believe Faith was his neighbor and lived in one of Toads apartments (Toad borrows things from his tenants and I believe him having donkeyskin coat is a solid proof). Faith didn't come to his apartment to offer her services - it would seem they only meet their clients in the hotel - but instead to look for something that want missing from hers - the stolen artifact. He was simply at the wrong place at the wrong time - and I think his role in future episodes will be a minor one.
That shifts our attention to Toad - I actually believe that he has the stolen artifact which he *borrowed * from Faith apartment right before the events of the first episode and will play a major role in future (maybe his son finds it?). I doubt that he's the killer though - he might have accessed mayors office in the past without anyone else knowing (he knows how to use the mirror to spy on others and we had a suggestion Toad added his his own description to one of the symbols in the book) and he might have a motive to dislike both the system and Bigby, but he'd rather carry on with the ongoing fable system than change things (for example he teaches his son to stay out of sight and avoid humans).
Next fable we are introduced to is Bluebeard. You have his file in your apartment, he is a former serial killer who decapitated his victims and you can name him a suspect very early in the game - but I believe it would just be too obvious and the game trows all that at us just to kick us off our tracks. Let's face it, he already is one of the wealthiest fables, fabletown government is in his pocket and he can influence it to his benefit - he gains nothing out of murders and especially out of Bigbys investigation, so I find it very unlikely for him to leave heads in front of sheriffs front door. Why does he act as he does during the interrogation during episode 2? Just his violent nature. I think he will still play a big role though, because with Crane gone he's the most likely person to jump at chance to take over (or try to) the deputy mayors position. Sure, becoming a mayor might be a possible motive, but I choose to believe that to this character it's just a fortunate - if you can call it that - situation which he can't simply slide.
And that brings us to our newest suspect, Ichabod Crane. He's a cowardly freak with sexual fantasies about Ms Snow, but I think by now everyone agrees that he's been framed - and I think all these murders were intentional just for his demise. First head was left on purpose for Bigby to find and start his investigation (I do believe that the stolen artifact has nothing to do with the murders and it's just 2 separate crime stories who happened to happen at the same time and confuse us), and envelope with photos was intentionally left at the second crime scene to bring down Crane. Smashing the mirror was a natural thing to do for Crane given the circumstances - he wouldn't want to be found. And I highly doubt that Crane would kill Lily - photos were obviously taken by someone else, and to be honest all we know is that he had sex with the troll (scared of diseases during body examination) - we didn't see any photos with him actually committing a crime. Why flee? He's a coward, and the shame of all these things going public would just be too much to bear.
Now before I carry on with my thoughts on individual characters, I'd like to point out some things about the murders. So far all we know for a fact is that both victims are decapitated and that they are working girls. We also know that fable prostitutes work for Georgie, they are afraid to talk because their lips are sealed and that they all are purple scarf bearers. My theory is that the scarf actually works as a leash and if one of the girls decides to talk, it does something really bad - and I'm pretty sure it is the way how both our victims literally lost their heads. if there is a spell to erase ones memory, like the one used by Crane at the start op episode 2, than I'm more than positive there is a spell to make someone talk/tell the truth - and once girls start talking, heads start rolling. That would also explain why there are no struggle marks on Lilys body - just one clean cut were scarf was supposed to be. It is also very important hint that the killer doesn't have to be big or strong - just smart. I wouldn't be surprised at all if very soon Little Mermaids head would show up as well - with another clean cut (I didn't read Fable comics, so I don't know whether she's alive or dead after events of the game, so I might be wrong on this), but in my opinion it would no longer do anything story wise.
Back to the characters. Another unlikable fella would be Georgie, but again I highly doubt he's the one to be a killer. First of all, there's no motive. It makes absolutely no sense for him to kill the prostitutes that already work for him - they bring him money, so he'd only be losing his income. Besides, he seems quite happy with his status and situation - why stir things up? To be honest after episode 2 I doubt he'll play any part in events yet to come (unless Little Mermaid does get killed after all). Sure, he might be a scumbag and treat girls like shite, but kill them? Nah...
Another character which I believe played his part and we won't see him anymore is Lawrence. The reason I'm saying this, he's already dead in most player games (last time I checked only ~30% went to his apartment first and had the chance to save him) - which makes it very unlikely that Telltale will spend any time on bringing him back into the story.
That leaves us with the last of the games suggested 5 prime suspects - the Tweedles. They do cross your path multiple times during first murder investigation, and as some people suggested they are the only characters besides Bigby who smoke - which apparently could tie them to 2nd crime scene - yet I believe they are indeed nothing more than hired goons to find the stolen artifact - which I again believe has nothing to do with the murders. They have no motive, and let's face it - they don't seem bright enough to pull something like that. They do redirect you to something more interesting though and I believe they still have a minor role to play in things to come.
Beauty and the The Beast. I doubt any of them is the killer, but there's definitely something bigger with then what we were shown so far. Why does the Beast show up in the hotel during your 2nd investigation? He does know what that place is, and he's shown like a guy who wouldn't cheat on his wife. Why would Beauty talk to Tweedles about Bigby and wheather he's a good guy or a scumbag if all she did was borrow money and they just come to extort it from her? Too many questions and not enough detail to deduce any viable answers - not yet. I'm 100% sure those two will play a major role in future episodes though.
I'm skipping Grendel, Holly and Bufkin because I don't think they are really worth noting. First two served their part to transit you from 1st murder to the 2nd - they helped you find Woody and redirected you to Georgie, but I don't really see any further use for them. And the flying monkey? I personally see him more like a static object - like a Mirror - who from time to time provides you with helpful information to get you back on your track. Besides, he doesn't seem to care about anything as long as he does have a bottle of booze.
Who I think is worth noting however is Jack. He was given a very trivial role so far, but I suspect he's the actual owner of stolen artifact and the mysterious employer of Tweedle brothers. That would actually explain why as soon as one of the brothers was released, instead of running back to his twin and lick his wounds he rushed to Jack instead and gave a rundown of events so far. And given Jacks fable background (running petty schemes to get rich) would give some insight on the artifact - maybe he finally found something that could actually work? I even have Jack as one of my suspects - Toad Jr mentioned that someone who dumped the body shouted "stop laughing at me!" - and it's certainly something Jack could say on a breakdown given other fables consider him a joke. Jack also think he's the most intelligent and important fable - which could explain why he dumped heads on Bigbys doorstep (Batman vs Riddler analogy, trying to prove to everyone that he's too smart to catch). He's not my first suspect choice though, and percentage wise I only give him 5% at max to be the killer, but we're to early into the story to be sure and in my opinion he's definitely a person of interest.
Another person of interest is Snow. Something just doesn't feel right about her. I'm quite positive she's not the killer, but there's way more to her than what we've been shown so far. She clearly states that she can stand up for herself and that she doesn't need protecting, she doesn't like Crane and whenever there's a crime she's always not too far away. She's shocked and saddened seeing the victims though - good acting or genuine feelings? I still choose to cross her out of my suspect list though - she is a crucial character, and as some people in the forum pointed out she does exist in comics that take place after the game, and I want to see her as a good gal more than a bad one - and I'm sure everyone will agree that she'll play a huge role in following episodes.
And that leaves me with one last character - who I'm 95% is the one we will find out to be behind all those killings and machinations - our good old buddy Colin. He's introduced very early into the game - and it is very often that the culprit is introduced at the very beginning of the story - he has a grudge against Bigby for destroying his home, and he simply hates mayor and the system which put him into the farm - which he says is more of a prison than home. He does wonder around town freely (Glamour user?) and somehow has easy access to both farm and other people apartments - he get's into sheriffs apartment without anyone noticing and it's clear it isn't his first time (someone who took those photos was watching Bigby close for some time). Another thing people failed to notice - pig was shown to smoke Huff'n'Puff - something that only Bigby smokes and something that is found in second crime scene. That also matches what Toad Jr heard - imagine a Troll be threatened by a pig - I know I'd laugh. Magic spell, troll talks, head rolls, pig is still mad that troll didn't take him seriously and sees her laughing face in his mind while dumping the body - seems plausible if you ask me. Another extremely important clue MAJOR SPOILER - trophy for completing chapter 2 of episode 5 is called "This House of Straw" - followed by "A Silver Bullet" and "My Last Cigarette" - which I assume implies that at the very end of the story you will be visiting your buddy Colin for one reason or another and it will be followed with a major confrontation which leaves Bigby in near dead situation - and if he has nothing to do with murders I don't really see any point to do such a thing.
If you read all of this, I want to thank you for your time and patience. I'm really loving this game so far and I sincerely hope future episodes will introduce something that makes all these theories obsolete - there are so very few games out there that are actually intriguing and make you think and try to notice small things, and this game definitively has a potential to be one of them. For me as a gamer there is no grater pleasure than to admit I've been mindfucked and creators managed to outsmart me and give me everything to figure the answer out, yet trick me into making wrong assumptions.
Cheers!